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A218476 Number of 3n-length 6-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word. 2
1, 1, 16, 331, 7746, 195011, 5153626, 140995716, 3958980906, 113434797571, 3303283462836, 97478710394451, 2908594804576416, 87605427983818356, 2659959016770389896, 81330226479826092536, 2501989790308939894026, 77386492111973937031491, 2405093253522796180052056 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*5^j for n>0, a(0) = 1.

Recurrence: 2*n*(2*n-1)*(9*n-11)*a(n) = 3*(2997*n^3 - 5769*n^2 + 2754*n - 200)*a(n-1) - 3240*(3*n-5)*(3*n-4)*(9*n-2)*a(n-2). - Vaclav Kotesovec, Aug 31 2014

a(n) ~ 3^(3*n-7/2) * 5^(n+1) / (sqrt(Pi) * n^(3/2) * 4^n). - Vaclav Kotesovec, Aug 31 2014

MAPLE

a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*5^j, j=0..n-1)/n):

seq(a(n), n=0..20);

CROSSREFS

Column k=6 of A213027.

Sequence in context: A246876 A176128 A223394 * A240344 A068368 A013993

Adjacent sequences:  A218473 A218474 A218475 * A218477 A218478 A218479

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 29 2012

STATUS

approved

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Last modified December 10 23:33 EST 2018. Contains 318049 sequences. (Running on oeis4.)